toeplitz.ipynb

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   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "597ffd84-ab0c-4d80-8734-cb1eef495b04",
   "metadata": {},
   "source": [
    "#### Construct a toeplitz matrix"
   ]
  },
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   "id": "1a9050b7-8fa8-40ce-80ec-e0ba7b27e4b0",
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   "source": [
    "x = np.zeros(50)\n",
    "x[0] = 2\n",
    "x[1] = -1\n",
    "x[-1] = -1\n",
    "A = sp.linalg.toeplitz(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "34984ba0-852e-4423-bac8-3492a2bc42a2",
   "metadata": {},
   "source": [
    "#### Calculate the eigenvalues and eigenvectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aefb9c65-ce26-4aaa-bb9b-3ada65413647",
   "metadata": {},
   "outputs": [],
   "source": [
    "v, w = sp.linalg.eig(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d18cc476-0904-43b4-9e0a-76eed3592163",
   "metadata": {},
   "source": [
    "#### Plot the lowest \"modes\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cbaaf37b-ed42-4d7a-993c-563287222416",
   "metadata": {},
   "outputs": [],
   "source": [
    "J = np.argsort(np.abs(v))\n",
    "for i in J[:6]:\n",
    "    plt.plot(w[:, i])"
   ]
  }
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